Skellam Type Processes of Order k and Beyond

In this article, we introduce the Skellam process of order k and its running average. We also discuss the time-changed Skellam process of order k. In particular, we discuss the space-fractional Skellam process and tempered space-fractional Skellam process via time changes in Skellam process by independent stable subordinator and tempered stable subordinator, respectively. We derive the marginal probabilities, Lévy measures, governing difference-differential equations of the introduced processes. Our results generalize the Skellam process and running average of Poisson process in several directions.     

Spectral Analysis of Fractional Hyperbolic Diffusion Equations with Random Data

Journal of Statistical Physics - The paper studies the fundamental solutions to fractional in time hyperbolic diffusion equation or telegraph equations and their properties. Then it derives the...     

Works of M. I. Yadrenko in the theory of random fields

A survey of the works of M. I. Yadrenko in the theory of random fields on finite-dimensional and infinite-dimensional spaces is presented.Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 44, No. 11, pp. 1460–1465, November. 1992.     

Estimators of regression parameters of random fields. II

We investigate asymptotic properties of modified least-square estimators (MLSE) of regression parameters of random fields.Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 44, No. 5, pp. 637–641, May, 1992.     

Limiting distributions of the solutions of the many-dimensional Bürgers equation with random initial data. II

We find non-Gaussian limiting distributions of the solutions of the many-dimensional Burgers equation with the initial condition given by a homogeneous isotropic Gaussian random ²-type field with strong dependence.Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 46, No. 8, pp. 1003–1010, August, 1994.     

Quantum chemical study of the intramolecular transfer of hydrogen in o- methylacetophenone and 1- alkylanthraquinones

The geometries and formation enthalpies of reagents, products, and triplet intermediates in the reaction of photoenolization of o- methylacetophenone and 1- methylanthraquinone are calculated by semiempirical quantum chemical methods. It is shown that the triplet intermediate is a triplet Σπ- biradical. The geometries and formation enthalpies of the transition state of the thermal transfer of the hydrogen atom in 9- hydroxy- 1,10- anthraquinone- 1- methide are calculated. The MNDO semiempirical methods give significantly exaggerated activation enthalpies in the thermal transfer of the hydrogen atom. Translated fromZhumal Strukturnoi Khimii, Vol. 38, No. 4, pp. 645–654, July–August, 1997.     

Tauberian and Abelian Theorems for Long-range Dependent Random Fields

This paper surveys Abelian and Tauberian theorems for long-range dependent random fields. We describe a framework for asymptotic behaviour of covariance functions or variances of averaged functionals of random fields at infinity and spectral densities at zero. The use of the theorems and their limitations are demonstrated through applications to some new and less-known examples of covariance functions of long-range dependent random fields.     

Vibrations of a Sandwich Rod under Local and Impulsive Forces

The forced vibrations of a sandwich rod under local impulsive surface loads and concentrated forces and moments are studied. The hypothesis of broken normal is used to describe the kinematics of the rod, which is asymmetric in thickness. The core is assumed to be rigid and compressible. An analytic solution is obtained and analyzed numerically __________ Translated from Prikladnaya Mekhanika, Vol. 41, No. 7, pp. 122–129, July 2005.